cotA / ( cosecA+1) + ( cosecA+1) / cotA = 2secA
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cotA/(cosecA+1) + (cosecA+1)/cotA
=cot²A+(cosecA+1)²/cotA(cosecA+1)
=(cot²A+cosec²A+1+2cosecA)/cotA(cosecA+1)
=(2cosec²A+2cosecA)/cotA(cosecA+1)
=2cosecA(cosecA+1)/cotA(cosecA+1)
=2cosecA/cotA
=2secA
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